Related papers: Core organization of directed complex networks
$k$-core decomposition is widely used to identify the center of a large network, it is a pruning process in which the nodes with degrees less than $k$ are recursively removed. Although the simplicity and effectiveness of this method…
We introduce a $k$-leaf removal algorithm as a generalization of the so-called leaf removal algorithm. In this pruning algorithm, vertices of degree smaller than $k$, together with their first nearest neighbors and all incident edges are…
The resilience of a complex interconnected system concerns the size of the macroscopic functioning node clusters after external perturbations based on a random or designed scheme. For a representation of the interconnected systems with…
With the development of complex networks, many researchers have paid greater attention to studying the control of complex networks over the last decade. Although some theoretical breakthroughs allow us to identify all driver nodes, we still…
We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the…
Multi-layer networks or multiplex networks are generally considered as the networks that have the same set of vertices but different types of edges. Multi-layer networks are especially useful when describing the systems with several kinds…
A number of important transport networks, such as the airline and trade networks of the world, exhibit a characteristic core-periphery structure, wherein a few nodes are highly interconnected and the rest of the network frays into a tree.…
Networks are ubiquitous in various fields, representing systems where nodes and their interconnections constitute their intricate structures. We introduce a network decomposition scheme to reveal multiscale core-periphery structures lurking…
A typical way in which network data is recorded is to measure all the interactions among a specified set of core nodes; this produces a graph containing this core together with a potentially larger set of fringe nodes that have links to the…
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi…
We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and…
We uncover the global organization of clustering in real complex networks. As it happens with other fundamental properties of networks such as the degree distribution, we find that real networks are neither completely random nor ordered…
Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy.…
We use the k-core decomposition to visualize large scale complex networks in two dimensions. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by…
An ordered graph is a graph enhanced with a linear order on the vertex set. An ordered graph is a core if it does not have an order-preserving homomorphism to a proper subgraph. We say that $H$ is the core of $G$ if (i) $H$ is a core, (ii)…
Among the novel metrics used to study the relative importance of nodes in complex networks, k-core decomposition has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system…
Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better…
Core-periphery structure is a common property of complex networks, which is a composition of tightly connected groups of core vertices and sparsely connected periphery vertices. This structure frequently emerges in traffic systems, biology,…
Profiling core-periphery structures in networks has attracted significant attention, leading to the development of various methods. Among these, the rich-core method is distinguished for being entirely parameter-free and scalable to large…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…